Determining Disk Version
You will need to look at the Zelda disk to see wich version you have. Use the table below to determine which version you have. On the back side of the disk you will see, in the outside of the center ring you will see text like "RZDE". This is what you need to look for to see to choose the right save slot. Use the table below to choose the correct one.

Begin by formatting your SD card to FAT16 if it is not already (in Windows it's just called "FAT"). FAT32 should also work in the latest release.

If you get an error such as "Failed to read boot.elf (-1)!" then reformatting your SD card with the Official SD Card Format Tool may help.

To do this on Mac OS X, open the Disk Utility (in Finder click the Go menu, select Utilities and find it there). Your SD card should show up as two entries. Choose the second entry, and then go to the Erase tab. Select the FAT16 option in the Volume Format dropdown, and assign a name to the device (if you want to), then click Erase. Confirm that you want to erase, and then follow the rest of this guide when it's done.

Copy the "private" directory from the download to the root your SD card.

Take your homebrew Wii executable (elf or dol file) and save it in the root directory of your SD card as "boot.elf" or "boot.dol" as appropriate.
If you would like to install the homebrew channel read the guide below, if not step this step.

Homebrew Channel Instructions

Download the files from the link above.

Once the Download is finished, extract the boot.elf and copy it into the root of your SD card.

Now, put the SD card into your Wii and turn it on.

Go into Wii Options --> Data Management --> Save Data --> Wii.

Find your Zelda save, click on it, click "Erase", and click Yes.

Open the SD card and select the "Twilight Hack" save that corresponds to your game region.

Click copy and then yes. Now exit out of the menu.

Insert The Legend of Zelda: Twilight Princess game disc and run the game.

To determine which save game you use the table and see above.

Once in the game, either walk backwards or talk to the man standing in front of you. And the homebrew will automatically start.

Homebrew Channel Instructions

You will be presented with a disclaimer screen about the dangers of installing
this hack (discussed here as well, below); follow the instructions.

After this process has completed, you should have a new Homebrew Channel in your System
Menu.

You may safely delete the boot.dol file from the SD card; it is no
longer needed.